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Geometry at Work

Each year, I am tasked with building props for my wife’s dance studio, NH Academie of Dance. This year, I had to build two giant hearts that were at least 10′ tall each. The original plan was that these hearts would consist of a wooden border about 6″ wide with white fabric stretched across the middle.

First, I decided that I was going to use MDF (Medium Density Fibreboard) for the heart border. MDF is often used for making furniture, school projects, etc., and it seemed like it would be a good choice for my needs. Strong, yet flexible.

The next step was to draw the heart to scale. I needed to be able to recreate the hearts on a large scale, so just drawing it freehand wasn’t really an option. It was time to dust off my high school geometry knowledge. Using a protractor and 45 degree triangle, I drew a half circle with a 2.5″ radius on a 45 degree angle (my original plans were hand drawn, but I’ve included some images below that I recreated on the computer for this post… the originals seemed more impressive to me… there’s just something about getting highly precise drawings by hand that looks more impressive). This would be the top left side of the heart.

Top left side of heart

Next, I created a mirror image of this by creating another half circle on a 135 degree angle. This angle was the tangent created at the rightmost edge of the first half circle. This gave me the top right side of the heart.

Top right side of heart

Next, I extended the tangents on the outer edge of each circle until they intersected to form the bottom of the heart.

Bottom of heart

I needed to know the lengths of the bottom pieces of the heart, so I took a look at what I knew already.

  1. The angles where the tangent lines crossed were all 90 degree angles so when dividing the heart in half down the middle, I get two right triangles, each with 45 degree angles for both of its complementary angles.
  2. If the complementary angles of a right triangle have the same measure, then the legs of the triangle opposite those angles have the same length. I knew that the radius of my arc was 2.5″, which meant that the diameter was 5″. Since the two 45 degree angles are equal, the lengths of both legs must therefore be 5″. I now had a scale version of my heart shape.

Heart with measurements

Looking back at it, I now see a much easier approach that I could have taken. I could have started by drawing a square, then draw the arcs using half the length of one side of the square as the radius, from the midpoint of one of the sides. Then I could have rotated the whole thing 45 degrees and it’s the same heart.

At this point, I had the basic outer edge of my heart shape. There was to be some overlap on the bottom (giving it an almost ribbon-like appearance), and at the top-middle of the heart where the arcs met. For the top overlap, I simply extended each arc along it’s tangent for about 9″ (since the width of the border was 6″, that gave about 3″ of overlap). For the bottom, I started out by creating an arc whose center was on one of the tangent lines (extending the tangents farther down), but in the end I decided that those could be a bit more freehand.

I was quite happy with the end result, and glad I still remembered some of those Geometry lessons from high school.

Posted in General, NH Academie of Dance.

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Web Hosting

I’ve been a loyal customer of HostMySite.com for many years. However, since they acquired Hosting.com, I feel the quality of customer support has been not quite as good as it once was. Also, the cost, while not unreasonable, is a little higher than I’d like to be paying (given the rough economy).

I’ve been considering moving to a new host. I’ve heard good things about JaguarPC.com, and the pricing looks great ($5 / month if I go with a 3 year plan).

Got any web hosts you’d like to suggest?

Posted in General, Web Development.

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Google Voice Turns 1 But Still Needs Fixing

http://googlevoiceblog.blogspot.com/2010/03/google-voice-turns-1.html

We wanted to thank you for letting us know what you think, and we hope you like the improvements we’ve made since then.

Many users have voiced their complaint about certain missing call screening features. In particular, I’m referring to the following:

  1. Once a call screening name has been recorded, there is no way to delete it or force it to be re-recorded. So if you friend calls you and hears the prompt to record his name and he says “What the F***?” as his name, that is what you will hear every time that person calls you. This is especially not good if you have little ones that might answer the phone.
  2. The proposed solution to that problem is not a solution at all. Add that person to your contacts and their name will be “read” instead. This is much more of a hack than a fix, and from what I’ve read it doesn’t even always work.
  3. Suppose the person is calling via a business that has a phone system that gives every outbound call the same caller id? For example, say my boss calls me from work and records his name. Now any time anyone calls me from that company, I will hear my bosses name even though it could be any number of people calling me.

It seems like a terrible oversight that users can not manage the recordings. Also, it should be configurable to force a recording every time for certain numbers (which would solve the 3rd problem listed above).

In my opinion, Google Voice still has a long way to go, and it’s disappointing that it has been live for a year with not even a word of fixing these issues.

Posted in General.

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Tasha Bit Me, and That Really Hurts

As I learned last night, it is never a good idea to try hand feeding a pill to a dog when that dog is still chewing on food.

As I stuck my left hand in her mouth (to hold it open while I popped the pill in with my right hand), I had my thumb too far back near the molars. As she continued chewing her food, she punctured right through the middle of my thumb’s fingernail with one of her pointy premolars. Blood instantly started flowing out of the hole, and the pain was intense. I washed it with antibacterial soap, and ran it under cold water for several minutes. Eventually the blood stopped flowing and I could see the small, purplish splotch in the center of my nail surrounding the crack. I put some antibiotic ointment on the wound and wrapped a bandaid around it.

A small amount of blood continues to make its way out of the hole in my nail today. I’m not sure yet whether that nail is going to fall off or not. A dull, throbbing pain continues, but it’s bearable. My impatience cost me, but I’ve learned my lesson. It was my fault, but I won’t make that mistake again.

http://www.youtube.com/watch?v=HE4FJL2IDEs

Posted in General.